The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.
Hence, option C) 9x + 5y = 7 is the correct answer.
What is the equation of line that passes through the points (-2,5) and (3,-4)?
Given the data in the question;
Point1 (-2,5)
Point2 (3,-4)
First, we determine the slope of the of the line,
m = (y₂-y₁)/(x₂-x₁)
m = ( -4-5 )/( 3-(-2) )
m = -9/5
Using the formula for equation, we determine the y-intercept
y = mx + b
Plug in the first point (-2,5) and the slope and then solve for the y-intercept b.
5 = -9/5(-2) + b
5 = 18/5 + b
b = 5 - 18/5
b = ( 25 - 18 )/5
b = 7/5
Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = -(9/5)x + 7/5
Convert to standard form
y = -(9/5)x + 7/5
Multiply each term by 5
5y = -9x + 7
5y + 9x = 7
9x + 5y = 7
The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.
Hence, option C) 9x + 5y = 7 is the correct answer.
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